Question

1
$y = x + 6$
$y = -2x - 3$
2

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( x + 6=-2x - 3 \)

Step2: Solve for \( x \)

Add \( 2x \) to both sides: \( x+2x + 6=-2x+2x - 3 \) which simplifies to \( 3x + 6=-3 \)
Subtract 6 from both sides: \( 3x+6 - 6=-3 - 6 \) which gives \( 3x=-9 \)
Divide both sides by 3: \( \frac{3x}{3}=\frac{-9}{3} \), so \( x = - 3 \)

Step3: Substitute \( x \) into one equation to find \( y \)

Use \( y=x + 6 \), substitute \( x=-3 \): \( y=-3 + 6=3 \)

Answer:

The solution to the system of equations is \( x=-3 \), \( y = 3 \) (the point of intersection is \( (-3,3) \))